Related papers: Second-Generation Wavelet-inspired Tensor Product …
We examine sparse grid quadrature on weighted tensor products (WTP) of reproducing kernel Hilbert spaces on products of the unit sphere, in the case of worst case quadrature error for rules with arbitrary quadrature weights. We describe a…
Image tokenizers map images to sequences of discrete tokens, and are a crucial component of autoregressive transformer-based image generation. The tokens are typically associated with spatial locations in the input image, arranged in raster…
Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…
We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…
This work develops extensions of Steffensen's method to provide new tools for solving the semi-blind image reverse filtering problem. Two extensions are presented: a parametric Steffensen's method for accelerating the Mann iteration, and a…
Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by…
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular…
The outer inverse of tensors plays increasingly significant roles in computational mathematics, numerical analysis, and other generalized inverses of tensors. In this paper, we compute outer inverses with prescribed ranges and kernels of a…
The Hadamard product of two tensors in the tensor-train (TT) format is a fundamental operation across various applications, such as TT-based function multiplication for nonlinear differential equations or convolutions. However, conventional…
Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding…
Fusing a hyperspectral image with a multispectral image acquired over the same scene, \textit{i.e.}, hyperspectral image super-resolution, has become a popular computational way to access the latent high-spatial-spectral-resolution image.…
High-performance multimode/multiwavelength (de)multiplexer is one of the most pivotal photonic devices for advanced on-chip interconnect systems. Traditional on-chip photonic (de)multiplexing requires large device footprint for maintaining…
We introduce a new topological coproduct $\Delta^{\psi}_{u}$ for quantum toroidal algebras $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in all untwisted types, leading to a well-defined tensor product on the category…
Diffusion model shows remarkable potential on sparse-view computed tomography (SVCT) reconstruction. However, when a network is trained on a limited sample space, its generalization capability may be constrained, which degrades performance…
We propose a novel approach for hyperspectral super-resolution, that is based on low-rank tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the correct recovery holds for a wide range of multilinear ranks.…
Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…
Variational Autoencoders (VAE) are probabilistic deep generative models underpinned by elegant theory, stable training processes, and meaningful manifold representations. However, they produce blurry images due to a lack of explicit…